Hermite Methods for Aeroacoustics: Recent Progress

Abstract

We present recent developments on Hermite methods for aeroacoustic simulations including time-stepping methods, hybridization with discontinuous Galerkin methods for handling of boundary conditions and adaptive implementations. By scaling studies reported below we show that the features unique to Hermite methods have promise to enable efficient exploitation of modern petascale architectures. We also present preliminary computations of turbulent jet noise obtained with the current implementation of our compressible Navier-Stokes solver.

An Analysis of Dispersion and Dissipation Properties of Hermite Methods and its Application to Direct Numerical Simulation of Jet Noise

“…Even for serial computations, we have shown that Hermite methods are more efficient than difference methods even in simple geometry for all but the least stringent error requirements. See, in particular, Figure 3 in Appelö et al 5…”

“…This paper will report on recent progress on the development, analysis and application of a class of methods known as Hermite methods 8 which are arbitrarily high order accurate, and very suitable for parallel architectures. This work is a continuation of our research program [3][4][5]9 on Hermite methods and their application to jet noise.…”

Variations on Hermite Methods for Wave Propagation

“…This is advantageous for high order or multi-stage timestepping methods compared to finite difference methods, where neighboring data must be accessed each time derivatives are approximated. This structure has also been noted to be well-suited for parallel implementations on modern architectures [2,11]. Hermite schemes, which were initially introduced for Cartesian domains, have also been coupled with discontinuous Galerkin (DG) schemes for numerical simulations on complex geometries [4].…”

“…Hermite schemes, which were initially introduced for Cartesian domains, have also been coupled with discontinuous Galerkin (DG) schemes for numerical simulations on complex geometries [4]. They have also been applied to problems in aeroacoustics [2], electromagnetics [4], and fluid dynamics [16].…”

Leapfrog Time-Stepping for Hermite Methods

“…To enable geometric flexibility, Hermite methods have been combined with discontinuous Galerkin methods [5]. Adaptive variants of Hermite methods have been introduced by means of padaptivity in [4], and preliminary work on h-adaptivity has been presented in [2]. Variations of the method which do not require a dual grid have been introduced in [15], and a flux conservative Hermite method has been introduced in [8].…”